| Great Britain. Civil Service Commission - 1880
...base and between the same parallels are equal to one another. Two equal triangles, ABC and DBG, are **upon the same base BC and upon the same side of it** ; prove that if AB be equal to AC the perimeter of ABC will be less than that of DBC. 4. If a straight... | |
| Euclides - 1881
...diagonal Equal tnanyles upon the same base, and uIton the tame side of it, art between the same paraUelt. **Let the equal triangles ABC, DBC, be upon the same base BC, and upon the same side of it.** The triangles ABC, DBC, are between the same parallels ; that is, if AD be joined, AD is parallel to... | |
| Education, Higher - 1884
...straight line are either two right angles, or together equal to two right angles. 11. Equal triangles on **the same base, and upon the same side of it, are between the same parallels.** AD is parallel to BC : AC and BD meet in E : BC is produced to P, so that the triangle PEB is equal... | |
| Education - 1882
...lines drawn from the vertex, one bisecting the vertical angle, the other perpendicular to the base. 2. **Equal triangles upon the same base and upon the same side of it, are between the same parallels.** Point out where the demonstration begins. History. 1. Explain the relations of Mary Stuart to the thrones... | |
| Marianne Nops - 1882
...— QED PROPOSITION XL. THEORBM. Equal triangles upon equal bases in the same straight line and on **the same side of it are between the same parallels. Let the equal** As ABC, DEF be on equal bases BC, EF, in A p 'the same straight line BF, and on the same side of it... | |
| Joseph Hughes - Education - 1883
...the three interior angles of every triangle are together equal to two right angles. Euclid, I., 2. 3. **Equal triangles upon the same base and upon the same side of it are between the same parallels.** Euclid, I., 39. Algebra. MALES. I. Add together i5-0 _ ii-*), 2дг- (3- 5^), and 2- (-4 + = I-I+IA... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 400 pages
...&c. QED PROPOSITION 40. THEOREM. Equal triangles, on equalbases, in the same straight line, and on **the same side of it, are between the same parallels. Let the equal triangles ABC,** DEF be on equal bases BC, EF, in the same straight line BF, and on the same side of it : they shall... | |
| Moffatt and Paige - 1883
...equal to the triangle DE F. Therefore, triangles upon equal bases, etc. Proposition XXXIX. Theorem. **Equal triangles upon the same base, and upon the same side of it, are** betwee-l the same parallels. Let the equal triangles ABC, DBC be upon the same base BC, and upon the... | |
| Euclides - 1884
...XXXVIII., that they divide the figure into four equal triangles. 87. PROPOSITION XXXIX.— THEOREM. **Equal triangles upon the same base and upon the same...Let the equal triangles ABC, DBC be upon the same** l>ase BC, and upon the same side of it. Then ABC and DBC shall be between the same parallels. Join... | |
| Edward Mann Langley, W. Seys Phillips - 1890 - 515 pages
...parallels. Let ABC and DEF be equal AS on equal bases BC and EF, in the same straight line BF, and on **the same side of it, they shall be between the same parallels. Join AD. AD shall be** || to BF. For if it is not, through A draw AG || to BF, meeting ED in G, [I. 31. and join GF. Then... | |
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